$A$ $B$ $C$ If: $ AC = 18$, $ BC = 4x + 3$, and $ AB = 6x + 5$, Find $BC$.
Answer: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {6x + 5} + {4x + 3} = {18}$ Combine like terms: $ 10x + 8 = {18}$ Subtract $8$ from both sides: $ 10x = 10$ Divide both sides by $10$ to find $x$ $ x = 1$ Substitute $1$ for $x$ in the expression that was given for $BC$ $ BC = 4({1}) + 3$ Simplify: $ {BC = 4 + 3}$ Simplify to find ${BC}$ : $ {BC = 7}$